With channels and the exchange acting as hub, you can do instant trades between altcoins.

This doesn't work with fiat accounts.  A "100% reserve" company could issue fiat tokens.  The exchange could then trade those tokens.

This eliminates the counter-party risk for the exchange.  If the exchange dies, you still have your (alt)coins and also fiat tokens.

There is still risk that the token company could go bankrupt though.  This could be mitigated by that company requiring only "cashing out" tokens to accounts which have been verified.

The company could set up a blockchain where it signed the blocks rather than mining and could get money from transaction fees and also minting fees (say it charges 1% for minting new tokens)

I wonder what how the law would work for that.  It isn't actually doing trading, it is just issuing tokens and redeeming them.